Uiua
Part 1 only for now, probably not the most optimal solution (calculating all possible rectangles) but at least it's short ^^
::spoiler Code
$ 7,1
$ 11,1
$ 11,7
$ 9,7
$ 9,5
$ 2,5
$ 2,3
$ 7,3
# &fras "input-9.txt" β
β(βββΈβ @,)βΈβ @\n
β§
<2
β‘(/Γ+β-ββ§β₯Β°β)
/β₯
:::

Using un-csv is smart :o
Much nicer to look at than the double partition I've been using so far
That part 2 scares me though :P